I had some problems in running Cortana on my PC/tablet updated to Windows 10 (even updating my Surface 3 pro that was in Italian!).

I found the following solution, that worked for me, in a thread of Microsoft Community forum:

It is used UK as example.

1. Click SETTING and then get into TIME&LANGUAGE

2. Click COUNTRY OR REGION

3. Change place to United Kingdom and add English(United Kingdom) as your default language.

4. Change you speech language to English(United Kingdom)

5. Click ‘Additional date, time & regional settings’

6. Change location to UK

7. (important step) After change location, do not close your page, just click Administrative and click Copy settings.

8. Tick all you can see and click OK

(VERY IMPORTANT)

If you see the language of Current user, Welcome screen and New user accounts are all English(United Kingdom), you will find Cortana work after you restart computer.

=====================

However I did not succeed to have Cortana works choosing Display/Input/Format language => English (US) and maintaining my real Location => another supported Country (e.g. Italy).

In fact I would like to maintain the UI of Windows to English (being a developer) but my location is Italy (not United States as I set the Display/Input/Format settings).

Therefore, for the time being, while if I put all setting to Italian/Italy Cortana works, if I try to set the UI to English and I leave my location to the real one (Italy), Cortana stops working (“Cortana is not supported in the region and language you’ve selected”). Waiting an answer from the community …

NOTE: you can use Cortana also if you are not logged with your Microsoft user (e.g. a local account). However be careful if you are using your Microsoft account and you use it on more PCs: in fact in that case it is better to disable the Language preferences synchronization. If you do not do so, if you put a different Windows display language in your PCs, possibly at the next reboot something wrong could happen on some of your PCs because of that synch with the setting of your account saved and synchronized with the cloud. You could have the Windows language changed or only some other language setting … and possibly have Cortana not work anymore on a PC where it worked (i.e. the one you put region and language compliant, like Italy and Italian). In that case even the voice recognition can fail as it is shown in the following screenshots.

Please make sure your Country or Region, Language and Speech Language settings are all aligned with one of Cortana’s supported locale configurations. If these OS settings are not aligned, Cortana will not be available. For example, Cortana will not be available if your country is set to United States, but the Windows display language is set to English (United Kingdom).

After the downloads are complete (this could take several minutes), return to the Time & Language settings

Click on your new language and select Set as Default.

NOTE: If you changed languages, you must sign out of your account and back in for the new setting to take effect.

Check the Country or region setting. Make sure the country selected corresponds with the Windows display language set in the Language setting.

Return to Settings and Time& language, and then select Speech. Check the Speech language setting, and make sure it’s aligned with the previous settings.

==========================

P.S.
4 Sept 2015 – In the following the Microsoft instructions sent today through the Insider Hub:

Setup Instructions

Cortana is available to Windows Insiders in the following configurations. In order for Cortana to be show up on your system, please ensure you system has the appropriate Country or Region, Language, and Speech Language select for your configuration.